Q1. Solve table 3

Based on TABLE 3,

1. Construct the probability distribution function of X.

(2 marks)

2. Construct the cumulative distribution function of X.

(2 marks)

3. Calculate the expected value of X. Interpret the value.

(3 marks)

4. Calculate the variance of X.

(4 marks)

5. Find the probability that the number of red candy is:
   1. less than the mean of X

(3 marks)

2. more than or equal to the mean of X

(3 marks)

3. between EX-1 and EX+1

Colour Total no. 2 no. 3 no. 4 no. 5 no. 6 20 TABLE 1: Number of candy by colour and by group member Group Group Group Group Group Group Member Member Member Member Member Member no. 1 27 24 27 29 31 24 27 20 20 27 29 25 23 24 27 18 26 36 30 28 25 29 27 18 31 128 128 129 131 128 128 green yellow red orange purple total Total 27 162 148 139 165 158 772 26 24 23 (3 Marks) TABLE 2: Total number of candy by colour Colour Total number of candy green 162 yellow 148 red 139 165 orange purple total 158 772 (1 marks) TABLE 3: Number of packs with X number of RED candy X Total f (3 marks) Colour Total no. 2 no. 3 no. 4 no. 5 no. 6 20 TABLE 1: Number of candy by colour and by group member Group Group Group Group Group Group Member Member Member Member Member Member no. 1 27 24 27 29 31 24 27 20 20 27 29 25 23 24 27 18 26 36 30 28 25 29 27 18 31 128 128 129 131 128 128 green yellow red orange purple total Total 27 162 148 139 165 158 772 26 24 23 (3 Marks) TABLE 2: Total number of candy by colour Colour Total number of candy green 162 yellow 148 red 139 165 orange purple total 158 772 (1 marks) TABLE 3: Number of packs with X number of RED candy X Total f